Preheat the oven to 350°F (175°C) and lightly grease a springform pan.
Toss the sliced apples with sugar and cinnamon in a bowl; set aside.
Mix flour, oats, and melted butter until crumbly, then press most into the pan for the crust, reserving ½ cup for topping.
Spread the apple mixture evenly over the crust.
Beat cream cheese, powdered sugar, and vanilla until smooth, then add eggs one at a time, mixing just until combined.
Pour the filling over the apples, sprinkle the reserved crumbs on top, and bake for 45–50 minutes until the center is set and the topping is golden.
Cool completely, then refrigerate for at least 3 hours before slicing.